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Cerebellar complex spikes multiplex complementary behavioral information

['Akshay Markanday', 'Hertie Institute For Clinical Brain Research', 'Tübingen', 'Graduate School Of Neural', 'Behavioral Sciences', 'International Max Planck Research School', 'Tübingen University', 'Junya Inoue', 'Werner Reichardt Centre For Integrative Neuroscience', 'Peter W. Dicke']

Date: 2021-10

Purkinje cell (PC) discharge, the only output of cerebellar cortex, involves 2 types of action potentials, high-frequency simple spikes (SSs) and low-frequency complex spikes (CSs). While there is consensus that SSs convey information needed to optimize movement kinematics, the function of CSs, determined by the PC’s climbing fiber input, remains controversial. While initially thought to be specialized in reporting information on motor error for the subsequent amendment of behavior, CSs seem to contribute to other aspects of motor behavior as well. When faced with the bewildering diversity of findings and views unraveled by highly specific tasks, one may wonder if there is just one true function with all the other attributions wrong? Or is the diversity of findings a reflection of distinct pools of PCs, each processing specific streams of information conveyed by climbing fibers? With these questions in mind, we recorded CSs from the monkey oculomotor vermis deploying a repetitive saccade task that entailed sizable motor errors as well as small amplitude saccades, correcting them. We demonstrate that, in addition to carrying error-related information, CSs carry information on the metrics of both primary and small corrective saccades in a time-specific manner, with changes in CS firing probability coupled with changes in CS duration. Furthermore, we also found CS activity that seemed to predict the upcoming events. Hence PCs receive a multiplexed climbing fiber input that merges complementary streams of information on the behavior, separable by the recipient PC because they are staggered in time.

It is a remarkable irony that CSs, notorious for extremely low discharge rates [ 28 – 33 ], hardly suitable to carry rich information, should accommodate such a diversity of behaviorally relevant signals. This, therefore, begs the question whether there is just one true function of CS with all the other attributions wrong, or are these different findings just a part of a larger puzzle? Could it be that we, cerebellar physiologists, share the fate of the blind monks in the ancient Indian parable, examining different parts of an elephant, each mistaking the respective part felt for the whole elephant? Alternatively, can the diversity of results, collected from different studies, be reconciled within a single task that may suggest that distinct pools of PCs might be recipients of specific streams of information conveyed by the climbing fibers? To answer these questions, we recorded CSs from the monkey oculomotor vermis (OMV) during a simple to and fro saccade task. By exploiting the natural variability in saccade endpoints that often evoked corrective saccades, we demonstrate that the same CS units that carry information on endpoint errors are also informative on primary and corrective saccade kinematics. We found that this information is represented not only by CS firing rates but also by CS duration. Additionally, we also found that a significant portion of CS units, which responded with a certain latency to trial onset, may predict the upcoming movement. We argue that probably every PC receives a multiplexed climbing fiber input that merges different and complementary streams of information on the behavior at stake, potentially separable by the recipient PC because they are staggered in time.

While several studies have been able to lend support to the MAI concept [ 4 – 14 ], others have unveiled features, not to be expected within this classical framework. For example, based on the clock-like regularity and precision of the firing of inferior olive neurons (the source of climbing fibers) Llinás and colleagues suggested a role of CSs in the temporal segmentation of movements [ 15 – 17 ]. Since then, many more observations on CS signaling have been made that require adaptations of the classical concept or even alternatives to it. For instance, studies on oculomotor adaptation in monkeys have suggested that CS discharge may not only initiate learning but, moreover, help to stabilize learning by reverberating information on past errors [ 18 – 20 ]. Fully compatible with this idea, also, experiments on eyeblink conditioning in mice have demonstrated that the same CSs that initially encode unexpected errors (air-puffs) also predict future errors by responding to a conditioned stimulus of a different sensory modality (LED or tone) reflecting information on past errors that serves as proxy of future errors [ 21 ]. Support for the role of CSs in encoding movement kinematics in addition to representing position errors comes from manual tracking experiments on monkeys [ 22 ]. Finally, more recently, yet another nonclassical role of CSs in conveying information on reward signals in a reactive and predictive manner has been put forward by studies involving visuomotor tracking experiments in mice [ 23 ] and smooth-pursuit eye movements in monkeys [ 24 ]. Additionally, it has also been shown that not only the CS firing probability but also its duration might be informative [ 25 ]. Yang and Lisberger [ 26 – 27 ] have argued that CS duration may indeed mediate error information instructing smooth-pursuit adaptation and suggested that instructive signals may adapt the spikelet architecture in a graded manner during motor learning.

The cerebellocortical Purkinje cell (PC) is unique in that it fires 2 types of action potentials, high-frequency simple spikes (SSs) and low-frequency complex spikes (CSs). SSs, which represent the integrated influence of information mediated via the mossy fiber-parallel fiber system and modulatory influences of interneurons, are fired at frequencies high enough to have an impact on target neurons outside the cerebellar cortex. They are thought to be the sole carrier of information allowing extracerebellar structures to optimize movement kinematics. CSs, on the other hand, are local manifestations of the second stream of input information conveyed by climbing fibers impinging onto target PCs. The strong excitatory influence of these CSs is thought to drive long-term plasticity at parallel fiber-to-PC synapses, which forms the basis of the first and arguably the most influential concept on the role of the climbing fiber input in reporting motor errors [ 1 – 3 ]. Within the framework of this Marr–Albus–Ito (MAI) concept, information on motor errors, conveyed via CSs, is used to drive motor learning by adjusting the PCs’ SS output to implement behavioral amendments necessary for avoiding the future reoccurrence of an error.

To test the relationship between sets of parameters encoded by CSs of individual PCs, we conducted a cross-correlation analysis. For this, we assigned a value of “1” if a given PC significantly encoded (p < 0.05) a particular parameter and a value “0,” otherwise. This allowed us to obtain an m × n matrix in which m represents the PC ID and n represents the individual parameter. We then computed a cross-correlation between individual columns (i.e., between different parameters) of this matrix to obtain the matrix of cross-correlation coefficients shown in Fig 8C .

To test for the encoding of a particular parameter/event (i.e., CP saccade offset relative to trial onset, primary saccade amplitude and direction, corrective saccade amplitude and direction, and error magnitude and direction) by CSs of individual PCs (see Fig 8B ), the distribution of the values of a particular parameter (for example, CP saccade offset relative to trial onset) was obtained, and its median value was then used to divide the distribution into 2 groups. The mean CS firing rates were then calculated for the 2 groups for distinct periods of interest (period of interest for trial onset–related CSs: 150 to 250 ms from trial onset; for saccade amplitude and direction: 0 to 100 ms from primary saccade offset; for corrective saccade amplitude and direction: 0 to 100 ms from corrective saccade offset; for error magnitude and direction: 50 to 250 ms from saccade offset; see Fig 1C ). The mean CS firing rates for the 2 groups for each parameter were then compared using a one-tailed Wilcoxon signed-rank test. For testing the directional preference for primary and corrective saccades, the mean firing rates from 0 to 100 ms from primary and corrective saccade offset, respectively, of the 2 opposite directions were compared using a one-tailed Wilcoxon signed-rank test. Differences were considered significant if p < 0.05.

To estimate the time of the trough, which was well aligned to the end of saccades and marked the beginning of CS modulation ( S2A Fig ), we randomly selected 1,000 trials of each duration bin (bin size = 5 ms) across all cells and computed the mean discharge rate. Then, we fitted a second order polynomial to the baseline period (−200 ms to 0 ms from saccade onset), and a linear function from the time of the peak back to −45 ms to the trough ( S2B Fig ). The intersection of these 2 functions gave us an estimate of the trough time for each iteration. This process was repeated 1,000 times, and the mean timing of the trough and its 95% confidence interval were estimated.

To capture the effects of saccade duration on the timing of CSs, we relied on the timing of the peak CS firing rate, as well as the timing of the trough. To calculate the peak time of the CS response, we randomly chose 50 PCs, each PC containing at least 10 trials for each duration bin (bin size = 5 ms) and calculated the mean firing rate and the time of the peak firing rate. By repeating this process 1,000 times, mean time of the peak and its 95% confidence intervals were estimated.

Since saccades were only made horizontally left or rightwards, the directions were binned into 2 broad classes having a size of 180° each. Interestingly, we did not observe the expected CS discharge in response to the large retinal error caused by the initial target jump. However, in most PCs, and as also reflected by the population response ( S2A Fig ), we observed the strongest modulation in CS activity developing around the time of the saccade end. We therefore determined CS’s preferred primary saccade direction based on the probability of CS firing for each direction by calculating the total number of CSs fired during the “early postsaccadic period” of 0 to 100 ms after saccade end (brown shaded region in Fig 1C ) and dividing them by the total number of saccades made in each direction. The direction with a higher mean probability of CS firing was defined as the preferred direction of the CS unit. For determining the preferred direction of corrective saccades, we calculated the firing rate during the “postcorrective saccadic period” of 0 to 100 ms from corrective saccade offset (purple shaded region in Fig 1C ). To determine each PC CS’s preferred direction of performance errors, we used the “precorrective saccadic period” of −200 to 0 ms from corrective saccade onset, which was similar to the “late postsaccadic period” lasting from 50 to 250 ms from primary saccade offset (green shaded region in Fig 1C ). In short, we refer to 3 postsaccadic periods of CS modulation: the primary saccade–related “early postsaccadic period,” the error-related “late postsaccadic period” (or “precorrective saccadic period”), and the corrective saccade–related “postcorrective saccadic period”.

The final identification of individual PC units relied on the demonstration of the 2 types of actions potentials they fire, the high-frequency SS discharge and the low-frequency CS discharge, and the verification that both originated from the same cell by documenting a 10- to 20-ms pause in SS firing following the occurrence of a CS [ 38 – 40 ]. Following a preliminary separation and characterization of CSs and SSs, carried out online using Alpha Omega Engineering’s Multi Spike Detector (MSD) needed to direct the experimental approach, the definitive analysis was based on an offline approach as described in detail by Markanday and colleagues [ 41 ]. In short, a deep neural network was trained to use relevant features of PC recordings that allow fast and reliable identification of CSs as well as characterization of their morphology including the detection of their start and end times. The algorithm relies on dividing the record into a high-pass spectral band (300 Hz to 3 KHz) suitable for the characterization of action potentials recordings and a lower frequency band (30 Hz to 400 Hz) for the characterization of LFP signals.

We performed extracellular recordings from PCs using glass-coated tungsten microelectrodes (impedance: 1 to 2 MΩ) that were purchased from Alpha Omega Engineering, Nazareth, Israel. The position of the electrodes, which were targeted toward the OMV, was controlled using a modular multielectrode manipulator (Electrode Positioning System and Multi-Channel Processor, Alpha Omega Engineering). The identity and the exact coordinates of the OMV predicted by the MRI scans were confirmed by physiological criteria, i.e., the presence of a dense saccade-related background activity, reflecting multiunit granule cells activity. To differentiate action potentials from the underlying LFP signals, extracellular potentials, recorded at the sampling rate of 25 KHz, were high band-pass filtered (300 Hz to 3 KHz) and low-pass filtered (30 Hz to 400 Hz), respectively. A total of 160 PCs were recorded out of which 151 were considered for analysis. A table summarizing the total number of PCs recorded from each monkey, either in left, right, or both directions, can be found in S1 Table .

(A) Experimental paradigm showing 2 separate sessions in which the rewarded CF saccades were made either toward the right (top panel) or left (bottom panel). And, in turn, the resulting CP saccades were made in the opposite direction. As shown in the illustrations, within a session, both CF (solid arrows) and CP (dashed arrows) saccades could either over- or undershoot the target location resulting in leftward (yellow arrows) and rightward errors (green arrows), respectively. Therefore, while saccades made in the same direction caused errors in opposite directions, saccades in opposite directions, for example, overshooting CF saccade to the right and undershooting CP saccade to the left could lead to errors in the same direction (i.e., leftward errors). (B) Histograms comparing peak velocity (left), duration (middle), and amplitude (right) of early (dark gray) and late (light gray) 30 trials of CF and CP saccades, pooled across 160 sessions. Solid vertical lines represent the median values. Vertical scale bars represent the number of sessions. (C) An illustration showing the temporal order of different events relative to saccade behavior (solid black trace) within a trial and the temporal relationship of various analytical periods, i.e., “early postsaccadic period” (brown shaded region; 0–100 ms from primary saccade offset), “late postsaccadic period” (green shaded region; 50–250 ms from primary saccade offset), and “postcorrective saccadic period” (purple shaded region; 0–100 ms from corrective saccade offset), relative to saccade behavior. Dashed lines indicate the position of the target dot at any given point in time. Note the overlap between the early and late postsaccadic period. (D) Response of an exemplary PC to left CF (blue) and right CP (red) saccades (upper panel). Raster plot (middle panel) of SSs (dots) and CSs (circles) and their corresponding mean (±SEM) firing rates (bottom panel) are shown in faded and bright colors, respectively. Note, how the probability of CS occurrence increases during the “early postsaccadic period” (gray shaded region, 0–100 ms from saccade end) for the rightward but not leftward saccades, suggesting that the PC’s preferred direction for primary saccades (PD ps ) pointed in the rightward direction. Also note, both CF and CP saccades were followed by errors in both directions (see variability in individual saccade trajectories). All data are aligned to saccade onset (dashed gray line). (E, F) CS population response (mean ± SEM; N = 151 PCs) in PC’s preferred (PD ps ) and antipreferred (PD ps +180°) direction (regardless of left, right, CF, and CP) of primary saccades (E, left panel) reveals a strong difference during the “early postsaccadic period” (gray shaded region), as compared to CS responses for primary saccades made in the left and right direction (F, left panel), regardless of CF and CP saccades. Inverted black triangles in E and F (left panels) represent the average saccade offset. All data are aligned to saccade onset (dashed gray line). Panels to the right in E and F show scatter plots highlighting individual differences between the PD ps and PD ps +180° and left and right directions. Each dot represents the mean of CS firing rate calculated during the “early postsaccadic period” for each PC. Gray dashed lines are the unity lines. Underlying data available from the Dryad Digital Repository: [ https://doi.org/10.5061/dryad.d51c5b03m ]. CF, centrifugal; CP, centripetal; CS, complex spike; PC, Purkinje cell; SS, simple spike.

We trained the 2 monkeys on a fatigue-inducing repetitive fast eye movements (saccades) task ( Fig 1A ). A trial was initiated whenever the monkeys moved their eye gaze into an invisible fixation window (2 × 2 deg) centered on a red fixation dot of diameter, 0.2 deg that was displayed at the center of a CRT monitor, placed at a distance of 38 cm in front of the subject. After a short fixation period varying from 400 to 600 ms relative to trial onset, the fixation dot disappeared and at the same time, a target appeared (go-signal) either on the left or—in other sessions—on the right at 15 deg eccentricity with features, matching to that of the fixation dot. In response, the monkey made a fast eye movement (saccade) toward the new target location, which was considered correct only if the eye gaze landed within an invisible fixation window (2 × 2 deg) centered on the target. Every center-out (= centrifugal (CF)) saccade ( Fig 1A , solid arrows) made correctly toward the target was rewarded with an instantaneously delivered drop of water. Approximately 700 to 900 ms after the go-signal, the peripheral target disappeared, and the central fixation dot reappeared. In order to proceed with the next CF trial, the monkeys readily executed short-latency back saccade from the peripheral target location to the fixation dot—centripetal (CP) saccades (dashed arrows)—although these CP saccades were not rewarded. As shown in Fig 1B (and S1 Fig ), the metric and kinematic structure of CP and CF saccades were very similar, their opposite directions notwithstanding, and both exhibited saccadic fatigue [ 37 ], characterized by a gradual drop in peak velocity, compensated by an increase of duration, keeping saccade amplitude stable. Although initially designed to induce a gradual decline in saccade velocities, another important aspect of the paradigm was that it allowed us to systematically tease apart the influences of postsaccadic errors from those of primary saccade kinematics on CS firing. This was possible because of the natural variability in primary saccade endpoints scattered around the target location ( S1C and S1D Fig ), which resulted in both over- and undershoots, often followed by corrective secondary saccades. The sequence of events relative to saccade behavior within a trial is conveyed by a schematic illustration in Fig 1C . The large number of trials that varied per session (median: 326 trials) depending on the motivation of the monkey to perform the task as well as on the time for which a PC could be kept well isolated further allowed us to reliably measure subtle changes in CS firing rates as well as changes in CS duration without resorting to any sophisticated statistical approaches. The duration of each trial was 1,200 ms. A Linux-based in-house software, NREC ( http://nrec.neurologie.uni-tuebingen.de ), was used to control the experiment and to collect and preprocess data.

Animals were trained to voluntarily enter an individually customized primate chair and get accustomed to the setup environment. After successful chair training, which could last for up to 3 months, the first major surgical procedure was conducted. During this procedure, titanium foundations of all implants were attached to the skull with titanium bone screws and allowed to rest under the subsequently reclosed skin for a period of approximately 3 to 4 months to ensure the long-term stability of the implant foundations. For the commencement of head fixation and experimental training, a titanium-based hexagonal tube-shaped head post was fixed to the base of the implanted head holder via the locally opened skin that allowed us to painlessly immobilize the head during experiments. At the same time, we implanted magnetic scleral search coils [ 34 , 35 ] to record eye position with high precision. After 2 to 3 weeks of recovery from the surgical procedures, monkeys were trained further on the tasks at stake. Once proficient, we opened the skin above the already implanted chamber foundation in order to attach the upper part of the cylindrical titanium recording chamber, tilting backward by an angle of 30° with respect to the frontal plane, right above the midline of the cerebellum and trepanated the skull within the confines of the chamber. The position and orientation of the chamber had been carefully planned based on presurgical MRI and was later confirmed by postsurgical MRI. This allowed reliable electrode access to our region of interest, the OMV (lobules VIc/VIIa). All surgical procedures were performed under aseptic conditions using general anesthesia (see Arnstein and colleagues [ 36 ] for more details). All vital physiological parameters (blood pressure, body temperature, heart rate, pO 2 , and pCO 2 ) were closely monitored. After surgery, analgesics (buprenorphine) were delivered to ensure painless recovery. Regular ethograms were recorded to keep track of monkeys’ progress until full recovery.

All neural and behavioral data used in this study were collected from 2 adult male rhesus macaques (Macaca mulatta), monkey K (age: 10 years) and monkey E (age: 8 years) that were purchased from the German Primate Center, Göttingen. All training, experiments, and surgical procedures abided by the rules set by German and European law as well as the National Institutes of Health’s Guide for the Care and Use of Laboratory Animals and were approved by the local authority (Regierungspräsidium Tübingen) for animal care under veterinary licenses N7/18 and N4/14. All procedures were carefully supervised by the veterinary service of Tübingen University.

Results

Velocity-duration adjustments and endpoint variability during repetitive saccade task In this study, we trained 2 rhesus monkeys to execute a long series of saccades toward a fixed target and back to the central starting location (Fig 1A). As expected, these stereotypic eye movements separated by short intertrial intervals of only 100 ms, caused a gradual decline in the vigor of saccades, arguably due to a gradual loss of interest over the course of trials. This “cognitive fatigue” [37], slowing down the pace of saccades, was compensated by an up-regulation of saccade duration sufficient to keep saccade endpoints within the required range of 2 deg around the target location at 15 deg eccentricity (see S1A and S1B Fig). Across all 160 recording sessions, we observed consistent effects as indicated by the averages (Fig 1B). Compared to the early (first 30) trials, the median peak velocity of both CF and CP saccades (Fig 1B, left panel) in the late (last 30) trials declined by 8.2% and 12.6% across all sessions, respectively (CF: early: 632.8 deg/s, late: 580.9 deg/s, Wilcoxon signed-rank test, p < 0.001, Z = 10.7; CP: early: 583.3 deg/s, late: 509.7 deg/s, Wilcoxon signed-rank test, p < 0.001, Z = 10.8). These changes were compensated by an increase of duration (Fig 1B, middle panel) of CF and CP saccades by 9.7% and 19.3%, respectively (CF: early: 39.9 ms, late: 43.8 ms, Wilcoxon signed-rank test, p < 0.001, Z = −10.7; CP: early: 43.3 ms, late: 51.7 ms, Wilcoxon signed-rank test, p < 0.001, Z = −10.8), thus keeping saccade amplitudes within an acceptable range of error (Fig 1B, right panel; CF: early: 14.7 deg, late: 14.6 deg, Wilcoxon signed-rank test, p = 0.02, Z = 2.2; CP: early: 14.8 deg, late: 14.9 deg, Wilcoxon signed-rank test, p = 0.03, Z = 2.1). Additionally, we also observed that the influence of fatigue, indicated by the amount of reduction in peak velocity, was stronger in the CP direction (12.6%) as compared to that of CF saccades (8.2%). Note that rewards followed the successful execution of CF saccades, whereas CP saccades were needed to get ready for a new trial, yet not followed by an immediate reward. Hence, the higher speed and shorter duration of CF saccades, their larger vigor, may be a consequence of more immediate reward expectations [42–46]. The natural endpoint variability in CF and CP saccades scattered around the target location (Fig 1B, right panel, S1C and S1D Fig) resulting in plenty of over- and undershoots that caused inward and outward retinal errors for each type of saccade. Therefore, for an exemplary session consisting of rightward CF and leftward CP saccades (see schematic diagram in Fig 1A), both inward and outward errors occurred in CF and CP direction. As will be discussed later, it is exactly this property that allowed us to tease apart the influence of primary saccades from their resulting errors on CS firing.

Complex spikes carry information on the direction, amplitude, and duration of the primary saccade Within a session, saccades could either over- or undershoot the target location resulting in both inward and outward retinal errors (Fig 1A). However, when comparing the CS firing rate for CF and CP saccades, we found clear saccade direction-dependent differences, regardless of the direction of the resulting errors. As demonstrated by the response of an example PC shown in Fig 1D, saccades to the right (CP in this case) were followed by a sharp increase in the CS firing during the postsaccadic period (0 to 100 ms after saccade end). Also, saccades in the opposite direction, CF saccades, were followed by an increased discharge. Yet, this increase was significantly weaker (peak firing rate ± SEM: CP = 5.97 ± 1.0 spikes/s; CF = 1.69 ± 0.5 spikes/s; Wilcoxon rank-sum test, p < 0.001, z = 4.20). We defined CSs’ preferred and antipreferred direction (PD ps and PD ps +180°, respectively) for primary saccades (subscript: ps) based on their activity during the “early postsaccadic period” of 0 to 100 ms relative to saccade offset (see brown shaded region in Fig 1C). The overall CS firing across all 151 PCs in their PD ps was clearly larger (Fig 1E, left) than to saccades made in the antipreferred direction (peak firing rate ± SEM: PD ps = 1.76 ± 0.11 spikes/s; PD ps +180° = 1.07 ± 0.08 spikes/s; Wilcoxon signed-rank test, p < 0.001, z = 6.38). One may argue that trying to assess a preferred direction based on just 2 opposite horizontal directions may fail in many cases because of insufficient sensitivity. Yet, as demonstrated by the scatter plot of individual PCs’ CS mean firing rate in the antipreferred direction as a function of the CS mean firing rate in the preferred direction (Fig 1E, right), this was clearly not the case, with just a handful of CSs lying on the unity line. On the other hand, a plot of early postsaccadic CS firing for right versus left saccades (CF and CP combined; Fig 1F, left) did not yield consistent preferences (Fig 1F, left; peak firing rate ± SEM: left = 1.34 ± 0.10 spikes/s; right = 1.46 ± 0.10 spikes/s; Wilcoxon signed-rank test, p = 0.43, z = 0.78 and Fig 1F, right). The notion that this difference reflected saccade direction rather than a preference for CP saccades is indicated by the fact that other PCs could fire more CSs for CF saccades with no consistent preference for CP or CF saccades in our sample (peak firing rate ± SEM: CF = 1.33 ± 0.09 spikes/s; CP = 1.45 ± 0.10 spikes/s; Wilcoxon signed-rank test, p = 0.99, z = 9.38; S2D Fig). It could also be objected that the strong CS discharge observed in the “early postsaccadic period” might be a consequence of the large retinal error generated by the target jumps. However, in the vast majority of PCs (83%), we did not observe any significant modulation during the period between 50 ms from target jump time to the time of primary saccade whereas—as said before—we typically observed a clear response closely following the end of the saccade, suggesting that the observed CS discharge was related to the primary saccade itself. The possibility of whether this response may reflect a postsaccadic retinal error will be discussed later. We further asked if the CS discharge for saccades made in the same direction yet starting from different positions differed from each other. To this end, we examined the CS responses of an exemplary PC, which could be tested for CF (and CP) saccades in both left and right directions during separate sessions. We found no difference in the CS peak firing rates for saccades with the same vectors but different points of origin (S2E and S2F Fig). We next explored the effects of saccade amplitude on the firing probability of CSs. To this end, we exploited the natural variability of saccade endpoints within the fixation window of ±2 deg centered on the target location (for CF saccades) and the fixation point (for CP saccades). Because of the shortage of primary saccades with amplitudes larger than 16 deg and smaller than 13 deg, we confined the analysis to a range of saccades between 13 to 16 deg, divided into equally spaced bins (bin size: 0.5 deg) and pooled across PD ps and PD ps +180° (i.e., CP and CF saccades in both left and right directions). As shown in Fig 2A, the maximum CS firing during the “early postsaccadic period” turned out to increase linearly with saccade amplitude (R-sq: 0.97; p = <0.001). To test the influence of saccade duration on CSs, we sorted the same pool of saccades into duration bins (range: 35 to 65 ms; bin size: 5 ms) and saw that longer duration saccades were associated with later population peak responses (Fig 2B; R-sq: 0.95; p = <0.001). Since the amplitude tended to increase with the duration of saccades, we also observed an increase in the CS firing for long-duration saccades. When aligning the CS population response to saccade offset (S2A Fig), we found that the postsaccadic increase in CS firing was preceded by a trough, a decrease in CS firing relative to the baseline level that at first glance seemed to indicate saccade end. This was indeed the case because also the timing of the trough (see Materials and methods for details; S2B Fig) proved to depend on saccade duration with trough times shifting with increasing saccade duration relative to saccade end (S2C Fig; R-sq: 0.86, p = 0.007). Surprisingly, considering the tight behavioral relationship between saccade velocity and duration, the firing probability of CSs turned out to be independent of saccadic peak velocity (Fig 2C; R-sq: 0; p = 0.99). We further investigated the effects of these kinematic parameters on CS firing individually in PD ps and PD ps +180° and found similar results (S3 Fig). In sum, CSs in our sample carried information on the direction of the primary saccade, its amplitude, and duration, yet not saccade velocity. PPT PowerPoint slide

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TIFF original image Download: Fig 2. CSs encode primary saccade amplitude and duration but not peak velocity during the “early postsaccadic period”. (A) CS population response (mean ± SEM) aligned to the onset of all primary saccades (PD ps and PD ps +180° combined) sorted by different amplitudes (left panel). The relationship between saccade amplitudes and peak firing rate of CSs is demonstrated with the help of a linear regression (right panel). (B) Population response (mean ± SEM) to saccades sorted by durations (left). The relationship between the timing of peak response (bootstrapped mean ± confidence intervals) and saccade duration is shown on the right. (C) Population response (mean ± SEM) to saccades with different velocities (left) and the corresponding regression plot (right). Green dotted lines represent the linear regression fits. The average saccade offset of each amplitude, duration, and peak velocity bin is denoted by inverted triangles in left panels. Note that the average onset of the upcoming corrective saccades occurred 349.2 ms after saccade onset. Underlying data available from the Dryad Digital Repository: [https://doi.org/10.5061/dryad.d51c5b03m]. CS, complex spike. https://doi.org/10.1371/journal.pbio.3001400.g002

Complex spikes carry information on corrective eye movements As a consequence of the inherent variability of saccade endpoints, causing retinal errors, saccades were followed by occasional secondary, corrective eye movements (amplitude: 0.2 to 2 deg) made toward the target location. As a matter of fact, we observed that the influence of these corrective saccades on CS firing was similar to the one of primary saccades. Fig 3A demonstrates the CS responses of an exemplary PC neuron (same PC as in Fig 1D) around the time of corrective saccades made during a single behavioral session. Trials, aligned with corrective saccade onset, were sorted according to the direction of the corrective saccade (left panels: corrective saccades to the left; right panels: to the right) regardless of their starting positions. No matter if the preceding primary saccade, ending approximately 272 ms before the corrective saccade onset, had been CP or CF, the CS firing rate increased within a period of about 100 ms from corrective saccade end (“postcorrective saccadic period”; see purple shaded region in Fig 1C). This is clearly depicted in the case of the exemplary PC’s CS response with a rightward preference for corrective saccades (Fig 3A) as exhibited by a strong discharge (peak firing rate: ± SEM: 6.25 ± 1.56 spikes/s) during the “postcorrective saccadic period” (Fig 3A; see raster plot and average CS response in the right panels), regardless of the preceding CF (red) or CP (green) saccades. In contrast, no clear modulation in CS firing was observed following corrective saccades to the left, the unit’s nonpreferred direction (peak firing rate ± SEM: 1.32 ± 0.92 spikes/s). Note, however, the increase in CS probability in the error period between primary saccade offset (inverted black triangle) and corrective saccade onset (Fig 3A, left panels); we will consider in more detail later. PPT PowerPoint slide

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TIFF original image Download: Fig 3. CSs encode corrective saccade direction, amplitude, and duration during the “postcorrective saccadic period”. (A) CS response of an exemplary PC to corrective saccades in leftward (left panels) and rightward direction (right panels). As illustrated by the schematic diagram on the top, supported by averaged (± SEM) saccade trajectories underneath, an experimental session with left CF (red) and right CP (green) saccades resulted in leftward corrective saccades that were made to correct the leftward error arising from CP saccades that “overshot” the fixation dot, and CF saccades that “undershot” the target location (left panel). The start and end positions of these corrective saccades were naturally different. Similarly, rightward corrective saccades resulted from overshooting CF and undershooting CP saccades (right panel). As seen in raster plots (middle panels) and the mean (± SEM) firing response of all trials (bottom panel), the peak firing rate of CSs was much larger for rightward (right panel) as compared to leftward (left panel) corrective saccades during the “postcorrective saccadic period” of 0–100 ms from corrective saccade end (gray shaded region). For each PC, CS’s preferred direction for corrective saccades (PD corr ) was based on this period. Note that neither the different starting positions of corrective saccades nor the direction of preceding primary saccades influenced the CS firing. The average time of the preceding CF saccade offsets (= 272 ms) and the upcoming CP saccade onsets (= 362 ms), relative to corrective saccade onset, is marked by inverted black and gray triangles, respectively. (B) CS population response (mean ± SEM; N = 151 PCs) sorted by PC’s preferred (PD corr ) and antipreferred (PD corr +180°) direction of corrective saccades based on “postcorrective saccadic period” (gray shaded region). Note that the CS activity during the “precorrective saccadic period” of approximately −200 to 0 ms from corrective saccade onset was used for determining the CS’s preferred direction of errors (PD error ). The average time of the preceding CF saccades offsets (= 305 ms) and the upcoming CP saccade onsets (= 331 ms), relative to corrective saccade onset, is marked by inverted black and gray triangles, respectively. (C) CS population response (mean ± SEM, PD corr and PD corr +180° combined) sorted by different amplitudes (left panel). The relationship between saccade amplitudes and peak firing rate of CSs is shown on the right. (D) CS response (mean ± SEM) to corrective saccades of different durations (left) and the corresponding relationship between the timing of peak response (bootstrapped mean ± confidence intervals) and saccade duration (right). Green dotted lines represent the linear regression fits. All data are aligned to corrective saccade onset. Underlying data available from the Dryad Digital Repository: [https://doi.org/10.5061/dryad.d51c5b03m]. CF, centrifugal; CP, centripetal; CS, complex spike; PC, Purkinje cell. https://doi.org/10.1371/journal.pbio.3001400.g003 As in the case of primary saccades, we compared the CS firing for corrective saccades made to the left and to the right, separated by using a bin size of 180°, in the “postcorrective saccadic period” of 0 to 100 ms from corrective saccade end. In other words, we only relied on the horizontal components of the corrective saccades in order to define their preferred and the antipreferred direction (PD corr and PD corr +180°, respectively, subscript corr: corrective saccades). We did this for each CS unit. The preferred direction of the corrective saccades corresponded to the preferred direction for primary saccades in only 42% of the PCs, i.e., a percentage that is close to the one to be expected in case of a random relationship of preferred directions for primary and for corrective saccades. Fig 3B depicts the population responses for corrective saccades made in the preferred and the antipreferred directions. Similar to the CS population response for primary saccades made into their preferred direction, we observed a clear peak of CS firing in the PD corr (peak firing rate ± SEM: PD corr = 2.33 ± 0.14 spikes/s; PD corr +180° = 0.93 ± 0.07 spikes/s; Wilcoxon signed-rank test, p < 0.001, z = 7.74) during the “postcorrective saccadic period” (gray shaded region in Fig 3B). However, in contrast to the CS population response to primary saccades in PD ps +180° (Fig 1E, green trace), the CS population response to corrective saccades in the PD corr +180° direction exhibited a broader discharge during the “precorrective saccadic period” of 200 ms from corrective saccade onset (Fig 3A, bottom left panel, and Fig 3B, orange trace). We will discuss the basis of the CS modulation during this period in detail later after having first considered the amplitude tuning of the postcorrective saccade CS response. To this end, we sorted all corrective saccades from all sessions in amplitude bins (bin size: 0.5 deg), pooling corrective saccades made in the PD corr and PD corr +180°, and plotted the CS peak firing rate as a function of corrective saccade amplitude. As shown in Fig 3C, this resulted in a clear postcorrective saccade peak whose size depended linearly on the amplitude (R-sq: 0.95, p = 0.027). This was also true when looking at the CS population responses separately for the PD corr and PD corr +180° (S4A–S4D Fig). Sorting corrective saccades based on duration, we observed that the peak of the CS population response occurred later if the corrective saccade took longer (Fig 3D; R-sq: 0.98, p = 0.081), a relationship that corresponds to the one for primary saccades. Further investigating the PD corr and PD corr +180° individually for effects of saccade duration on the CS timing revealed similar patterns in both cases (S4E–S4J Fig). Moreover, even the timing of modulation onsets (“troughs”) shifted with corrective saccade durations (S4 and S4J Fig). Our results on corrective saccades clearly indicate that CSs carry precise information on corrective saccade amplitudes and timing in the “postcorrective saccadic period” in a manner that is very similar to information on primary saccades in the “early postsaccadic period.”

Complex spikes convey error-related information As mentioned in the previous section, we also observed an increase in CS firing for corrective saccades in PD corr +180° −200 to 0 ms from corrective saccade onset (Fig 3B, orange trace). Could it be that this modulation that starts building up around the end of preceding primary saccades (Fig 3B, mean saccade end = 305.2 ms; inverted black triangle) is simply a delayed response to the preceding primary saccades as discussed in the earlier sections? Or was it related to retinal errors resulting from imprecise primary saccades prompting subsequent corrective saccades? To explore this alternative, we sorted all primary saccades recorded for a given PC according to the direction of the retinal error, i.e., the vector pointing from the primary saccade end toward the target location, ignoring primary saccade directions and their starting points (see illustration in Fig 1A). The error direction for which higher CS firing was observed in the “precorrective saccadic period” was labeled PD error and the opposite direction, PD error +180°. For each PC, we calculated CS responses to primary saccades that caused errors in PD error and PD error +180°, respectively, to compute CS population responses for these 2 directions. As shown in Fig 4A, the population averages differed in this “early post saccadic period” with the average in the preferred error direction characterized by a “burst-tonic” profile (red trace), starting to deviate from the population average for the opposite direction (purple trace) a few 10 ms after saccade offset, exhibiting a peak firing rate about 50 ms after saccade offset and staying elevated until well after 200 ms. Note that, also, the profile for the opposite direction showed an early peak while lacking the later tonic response component. PPT PowerPoint slide

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TIFF original image Download: Fig 4. CSs encode the retinal error direction and magnitude during the “late postsaccadic period” in a manner different from primary and corrective saccades. (A) CS population response (mean ± SEM) aligned to the offset of primary saccades made in the preferred and antipreferred direction of errors (PD error , red; PD error +180°, purple) and primary saccades (PD ps , brown; PD ps +180°, green). Note the differences between CS responses in PD ps and PD ps +180° are confined to the “early postsaccadic period” (gray shaded region). Note that the average onset of the upcoming corrective saccades was 305 ms relative to primary saccade offset. (B) Difference between the CS responses in PD error and PD error +180° (blue) and PD ps and PD ps +180° (orange). The influence of sorting CSs by PD error can be seen as the separation of the curves during the “late postsaccadic period” of 50–250 ms from saccade offset (gray shaded region). (C) Left panel illustrates errors of different sizes (colored arrows) in PD error and PD error +180° resulting from saccades of different amplitudes (black arrows) made in both directions. Saccades resulting in comparable error vectors were combined (for example, see gray arrows) to test the influence of size and direction of errors on CS firing. Right panel highlights the relationship between different error sizes and mean CS firing (± SEM) during the “precorrective saccadic period.” Note how the same error magnitude (see blue and gray) evokes a strong and a weak CS discharge depending on whether this error occurred in the preferred or antipreferred direction, respectively, thus showing a clear influence of error direction on CS firing. The inset demonstrates the same relationship when mean CS firing was calculated during the “late postsaccadic period” of 50–200 ms after saccade end. (D) Primary saccades of different amplitudes (colored arrows) in PD ps and PD ps +180° (left panel) and their corresponding influence on the peak firing rate (mean ± SEM) during the “early postsaccadic period” (right). (E) Corrective saccades of different amplitudes (colored arrows) in PD corr and PD corr +180° (left) and their corresponding influence on the peak firing rate (mean ± SEM) during the “early postcorrective saccadic period” (right). Dashed gray lines represent the linear regression fits. Underlying data available from the Dryad Digital Repository: [https://doi.org/10.5061/dryad.d51c5b03m]. CS, complex spike. https://doi.org/10.1371/journal.pbio.3001400.g004 When sorted by the preferred direction of primary saccades, the population averages exhibited an early peak, significantly larger in the preferred saccade direction (Fig 4A, brown trace). Yet, the averages for the preferred and the antipreferred directions lacked any difference later, during the “late postsaccadic period” of 50 to 250 ms from primary saccade offset, falling back to baseline level already after only 113 ms. The contrast between the population averages sorted by retinal error as opposed to the averages sorted by primary saccade direction becomes particularly apparent when comparing the respective difference plots for the preferred and the antipreferred directions (Fig 4B), clearly demonstrating that the later modulation of CS firing is error specific and independent of the metric of the primary saccade. The possibility that this modulation might be influenced by the upcoming corrective saccades can also be excluded based on the fact that the average corrective saccade onset occurred much later, approximately 305 ms after primary saccade offset. We wondered if the influence of error on the CS firing during this period is graded, reflecting not only an influence of direction but also of error magnitude. To find an answer, we sorted the CS population responses for corrective saccades into retinal error magnitude bins (bin size: 0.5 deg; Fig 4C, left) calculated for the “precorrective saccadic period” (200 ms before corrective saccade onset). As shown in Fig 4C, the mean firing rate of CSs increased with an increase in error magnitude in the PD error ; however, in the opposite direction, CS firing decreased as the error magnitude increased (Fig 4C). In other words, a large error in PD error triggered a stronger CS discharge, whereas the same magnitude of an error made in PD error +180° evoked a weaker CS discharge, thereby establishing a monotonic increase (R-sq: 0.92; p < 0.001) in CS firing as errors changed their magnitudes from antipreferred to preferred direction. We observed a similar pattern of CS firing rates during the “late postsaccadic period” of primary saccades, when sorted by error magnitude (see inset in Fig 4C; R-sq: 0.91; p < 0.001), clearly indicating that the “precorrective saccadic period” and “late postsaccadic period’ shared the same error-related information and establishing that error influences CS firing in a graded manner. As demonstrated earlier, primary saccade amplitude modulates CS firing in the “early postsaccadic period.” However, unlike the influence of error magnitude—which is opposite for errors in the preferred and the antipreferred direction—the influence on firing in the “early postsaccadic period” turned out to be the same for the 2 directions. For both primary saccades (Fig 4D) and for corrective saccades (Fig 4E), discharge increased with amplitude, no matter if saccades were made in the preferred or the antipreferred direction, respectively (PD ps : R-sq: 0.97, p < 0.001; PD ps +180°: R-sq: 0.96, p < 0.001; PD corr : R-sq: 0.97, p = 0.015; PD corr +180°: R-sq: 0.9, p = 0.053), with a relatively larger discharge in the preferred directions. However, note that the amplitude tuning could not be assessed across the whole range of amplitudes tested. This is clearly indicated by the fact that, in absolute terms, the CS firing associated with corrective saccades was clearly not weaker than the firing associated with the much larger primary saccades. Hence, in addition to direction and amplitude, the discharge in the “early postsaccadic period” is also determined by saccade type.

Complex spike duration encodes error- and saccade-related information It has been argued earlier that not only the probability of CSs firing but also systematic changes in CS duration, the latter being dependent on the “state” of the olivary neurons determining the strength of the climbing fiber input [47,48], carry behaviorally relevant information necessary to drive motor learning [26,27]. To test the relevance of CS duration in our task, we measured the duration of individual CSs fired by each PC as the time between CS start and end, by deploying an interactive deep neural network [41]. As shown for an exemplary PC neuron (Fig 6A), we found a bimodal distribution of CS durations for a single behavioral session. Taking a closer look at the CSs in the 2 modes revealed that the longer duration CSs (mean duration of CS: 6 ms) were characterized by a waveform with an additional spikelet at the end, not exhibited by CSs in the short duration mode (mean duration of CS: 4.2 ms). There was no change in the shape of the initial fast-spiking component (Fig 6B). PPT PowerPoint slide

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TIFF original image Download: Fig 6. Changes in CS duration encode changes in primary and corrective saccades as well as errors. (A) Histogram showing a bimodal distribution of CS durations in an exemplary PC. For illustration purposes, we separated the distribution into long and short duration CSs by eye (vertical dashed line). Solid vertical lines represent the median value of short (blue) and long (dark yellow) duration CSs. (B) Averaged (± SEM) waveforms of long and short duration CSs. (C) Population response (mean ± SEM) showing percentage change in CS duration aligned to primary saccade onset, for large (dark yellow) and small (blue) amplitude saccades. The population response was obtained from running averages of percentage change in CS duration, computed for every 50 ms bins, relative to the mean CS duration of each PC. (D) Percentage change in CS duration during the 100–200 ms period from primary saccade onset (gray shaded region in C) relative to saccade amplitudes in PD ps and PD ps +180°. (E) Percentage change in CS duration for primary saccades made in PD error and PD error +180°. Data aligned to primary saccade end. (F) Percentage change in CS duration relative to error magnitudes in PD error and PD error +180° during the 50–250 ms period from saccade offset. (G, H) Same as C and D, except for corrective saccade. (I) Percentage change in CS duration for corrective saccades in PD error and PD error +180°. (J) Percentage change in CS duration relative to error magnitudes in PD error and PD error +180° during the −250–0 ms period from corrective saccade onset. Data in G and I aligned to corrective saccade onset. Error bars and dashed gray lines in D, F, H, and J represent the SEM and fits based on linear regression, respectively. Significant differences between CS responses in C, E, G, and I are indicated by asterisks. Underlying data available from the Dryad Digital Repository: [https://doi.org/10.5061/dryad.d51c5b03m]. CS, complex spike; PC, Purkinje cell. https://doi.org/10.1371/journal.pbio.3001400.g006 To investigate task-related changes in CS duration, we computed a running average (bin size: 50 ms) of percentage change in CS duration relative to mean CS duration of an individual PC and estimated a population-based percentage change in CS duration. This population measure showed a conspicuous drop relative to baseline (peak change from baseline: 7.5%) in the perisaccadic period. In the subsequent phase, the population CS duration increased again, reaching a maximum value of 1.6%, about 100 ms after primary saccade end. When comparing the trajectory of duration changes with the one for CS firing rate (S8 Fig), it became clear that the two were obviously yoked, with decreases in duration roughly paralleling decreases in CS probability and vice versa. Therefore, given that the postsaccadic CS discharge is modulated by changes in saccade amplitude and error size, we asked if CS duration carried this information in similar periods. To this end, we compared mean CS duration changes in the early and late postsaccadic periods (gray shaded regions in Fig 6) for changes in primary and corrective saccade amplitudes, as well as errors. When sorting primary saccades by their amplitudes, it became apparent that the CS duration changes for larger amplitude saccades (mean amplitude: 16.4 deg) differed from those for smaller amplitude saccades (mean amplitude: 13.7 deg) in the postsaccadic period (Wilcoxon signed-rank test, p < 0.001, z = 8.72), of 100 to 200 ms after saccade onset, i.e., approximately 50 to 100 ms after saccade end (Fig 6C). As shown in Fig 6D, the percentage change in CS duration during the postsaccadic period increased with primary saccade amplitude (bin size: 1 deg), independent of saccade direction (PD ps : R-sq = 0.98, p = 0.011; PD ps +180°: R-sq = 0.99, p = 0.007), a pattern very similar to the amplitude tuning obtained for CS firing rates (Fig 4D). Distinguishing primary saccades based on their preferred error direction (i.e., PD error versus PD error +180°; Wilcoxon signed-rank test, p < 0.001, z = 12.29; Fig 6E), we observed that CS duration grew in the error period for saccades causing larger errors in the preferred error direction and dropped in the opposite direction (Fig 6F; R-sq = 0.99, p = 0.0014), a pattern reminiscent of the one observed for CS firing rates in response to error magnitudes (Fig 4C). Similar to the dependence of CS firing on the size of corrective saccades (Fig 4E), we found that CS durations increased with corrective saccade amplitude (Fig 6G, Wilcoxon signed-rank test, p < 0.001, z = 5.1), regardless of their direction (i.e., PD corr and PD corr +180°; PD corr : R-sq = 0.89, p = 0.215; PD corr +180°: R-sq = 0.99, p = 0.069; Fig 6H). Note that for the comparison of mean CS duration changes for different amplitudes of primary and corrective saccades (gray shaded regions in Fig 6C and 6G), we slightly delayed the beginning of these periods, relative to the “early postsaccadic period,” in order to highlight subtle changes in CS duration. Finally, the influence of error magnitude on CS duration before the corrective saccade (Fig 6I; Wilcoxon signed-rank test, p < 0.001, z = 7.57) was similar to the one for primary saccades in preferred and antipreferred error directions (Fig 6J; R-sq = 0.95, p = 0.026). Together, these findings clearly suggest that CSs convey saccade- and error-related information by duration changes that parallel changes in CS firing rates.

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